Our motivation follows from simple 3D RT computations. It can be shown numerically—and in some cases analytically—that, in the absence of absorption, the ratio of overall reflected flux *R* to overall transmitted flux *T *(= 1–*R*) increases in proportion with optical thickness τ, at least if it is large enough (≥10) to describe an opaque cumulus-type cloud. In fact *R/T* is commensurate with the scaled optical depth (1–*g*)τ where *g* is the asymmetry factor of the scattering phase function. For 3D clouds, τ is measured along a diameter, or it can be redefined as an average over the cloud area perpendicular to the solar illumination. We will show that this simple *R/T* ~ (1–*g*)τ law can be generalized to arbitrarily shaped internally uniform clouds with convex geometry and sufficient opacity. Note that the *R* vs. *T* partition is based here on the illuminated–versus-shaded separation at the terminator line, and not on angle away from the vertical as is customary in climate studies. So some of *R* goes to the ground, and some of *T* goes to space.

Can this finding be exploited in cloud remote sensing? Can we thus break away from the 1D RT paradigm? In view of the above, the trick is to estimate *R/T* from the observations. In a sense, this is easy if we have exquisite spatial resolution (say, on the order of ASTER's 15-m pixels) because pixels will have either purely transmitted light or purely reflected light depending on which side of the cloud's terminator they fall; see Davis' (2002) illustration with the DOE Multispectral Thermal Imager (MTI) satellite. On the other hand, it isn't clear that the *R* and *T* pixels selected in the image, presumably by hand, will be representative of the overall *R* and *T* values. Furthermore, we are interested in at least semi-automated approaches applicable to sensors with moderate spatial resolution since they have swaths wide enough to provide global coverage. However, the majority of these larger pixels for a single isolated cloud will be mixtures of radiance originating as *R*, as *T* and from the clear air and surface. Such mixtures must first be unraveled from the known scattering angle and a first-order approximation to the cloud's finite geometry. We have opted for a geometric primitive in the form of scalene hemi-ellipsoids: flat base, rounded top with arbitrary semi-axes (*a,b,c*), height above the surface, and horizontal orientation w.r.t. the sun.

For individual clouds, MISR's multi-angle imaging capability has so far been used only for geometric (height) and kinematic (wind) retrievals based on automated feature recognition and stereoscopic techniques. With its 275-m pixels at all 9 angles (at least in the red channel), MISR also offers the best opportunity to develop a radiometric *R/T* algorithm. We will show that various views of the same cloud lead to a reasonably robust estimate of the fluxes *R* and *T* in relative units (absolute radiometric calibration is in fact optional) along with other geometrical parameters. Given the solar zenith and azimuthal angles, we can derive the effective t from the *R/T* ratio and associated approximate cloud geometry (*a,b,c*) and orientation fitted to the data.

In a second step, we use the fitted geometric primitive shape and opacity for the cloud as initial guesses for an iterative adjustment of the cloud's outer shape and density that will improve the fit to the observed radiances. At this stage, we continue to assume the cloud is radiatively diffusive and internally uniform. That way, we can use a fast numerical solver for Laplace's equation in a 3D domain with a varying upper boundary defined on an unstructured mesh. Currently, an end-to-end demonstration of the cumulus cloud reconstruction is being performed in 2D. Extension to 3D will require more effort.

Applications for such radiometrically correct characterizations of finite isolated clouds abound. For instance, the first stage alone may be good enough to enable previously impossible remote sensing of clear air (aerosols, gases) and surface properties in close vicinity of clouds, i.e., accounting for strong cloud adjacency effects. Accurate cumulus cloud and joint cloud/aerosol retrievals, as required to properly address various indirect aerosol effects on climate, will certainly call for the second stage.

*References:*

A. B. Davis (2002), Cloud remote sensing with sideways-looks: Theory and first results using Multispectral Thermal Imager data, *S.P.I.E. Proceedings*, **4725***, *397 – 405.

Várnai, T., and A. Marshak (2002), Observations and analysis of three-dimensional radiative effects that influence MODIS cloud optical thickness retrievals, *J. Atmos. Sci.*, **59**, 1607 – 1618.